Darboux, Moser and Weinstein theorems for prequantum systems and applications to geometric quantization

We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symple...

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Detalles Bibliográficos
Autores: Miranda, E., Weistman, J.
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/479377
Acceso en línea:http://hdl.handle.net/2072/479377
Access Level:acceso abierto
Palabra clave:Prequantum systems
Quantization
Real polarization
Darboux-Weinstein-Moser theorem
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Descripción
Sumario:We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symplectomorphism and a gauge transformation. As an application, we show that the Bohr-Sommerfeld quantization of a prequantum system on a manifold with trivial first cohomology is independent of the choice of the connection.